A design method for polarization-multiplexed dual-channel meta-lens

Abstract

The present invention discloses a design method for a polarization-multiplexed dual-channel meta-lens, which establishes a mapping relationship between geometric structure parameters and optical responses through a deep neural network. Starting from the phase profile requirements required for dual-channel meta-lens imaging, the required structural parameters are obtained with the help of an inverse neural network, and the performance of the device is quickly evaluated through a forward neural network. The method of the present invention is flexible in design and can quickly complete the design of a meta-lens based on the required working wavelength, multiplexed polarization channels, and multi-focal space coordinates. The method of the present invention can be applied to the structural design of optical devices under multi-function or multi-constraint conditions, and has the advantages of high flexibility, strong robustness, wide applicability, and fast calculation speed. It has important guiding significance for the design of complex multi-function optical devices.

Description

Technical Field

[0001] The present invention relates to a design method for a polarization-multiplexed dual-channel metalens, and more specifically to a design method that utilizes a forward prediction neural network and an inverse generative neural network to solve the design requirements of the dual-channel metalens through the inverse generative network to obtain the parameters of the unit structure to meet its target optical requirements and achieve the expected focusing function. Background Art

[0002] Metasurfaces are planar optical devices composed of subwavelength-scale unit structures. By leveraging the structural parameters of their unit structures, the interaction between light and structure can be manipulated at subwavelength scales. Due to their significant advantages, including strong light manipulation capabilities, thin device thickness, high unit integration, and simple processing, metasurfaces are widely used in sensing, imaging, communications, and other fields. In particular, metasurfaces used for focused imaging are also known as metalenses. Through more sophisticated design, metasurfaces can simultaneously manipulate multiple optical properties to achieve multiple functions, holding great potential in emerging fields such as high-throughput encrypted communications and multi-channel optical imaging. Common multifunctional metasurfaces achieve this by multiplexing various optical properties, such as angular momentum, polarization, and wavelength. Compared to single-function metasurfaces, multifunctional metasurfaces require the manipulation of light in multiple dimensions. Classic multifunctional metasurfaces are achieved through segmented, staggered, or multi-layered designs. While this approach is simple, it results in low device efficiency and high background noise. Another solution is to use the same set of nanounit structures to achieve different optical requirements, thereby obtaining a high-efficiency, low-noise metasurface, which poses a huge challenge to the design of nanostructures.

[0003] Reverse engineering, a classic design strategy, focuses on finding an effective algorithm to translate desired properties into a specific physical system, based on the target requirements. In optical design, this strategy can be used to identify the desired optical performance and then search for suitable structures within the design space that meet the requirements. To achieve optimal device performance, the design space often has a large degree of freedom. To more efficiently explore the design space, the classic reverse design process is often guided by optimization algorithms, such as topology optimization, genetic algorithms, and particle swarm optimization. These algorithmic optimization processes require verification of device performance and continuous iterative updates, which consumes significant resources.

[0004] Artificial intelligence algorithms, such as deep neural networks, consist of a large number of logical computing nodes that resemble biological neurons. By adjusting the weights and biases of these computing nodes, they minimize the error between the deep neural network and the given target output data, thereby automatically learning the inherent patterns and connections from the data. Over the past decade, deep learning has been increasingly introduced into interdisciplinary research, such as quantum optics, protein structure analysis, and computational imaging. Compared to classic reverse engineering strategies, deep learning can automatically discover useful information from data and then construct a mapping relationship between input and output data. Thanks to its powerful data processing capabilities, deep learning has brought development opportunities to many photonics research fields, such as spectral analysis, device reverse engineering, and imaging system optimization. Summary of the Invention

[0005] The present invention aims to provide a design method for a dual-channel metalens. Starting from the phase profile requirements for dual-channel metalens imaging, this method uses an inverse neural network to obtain the required structural parameters and complete device design. Furthermore, a forward neural network can be used to rapidly evaluate the focusing performance of the device. This method offers flexibility and can rapidly complete design based on the required operating wavelength, multiplexed polarization channels, and multi-focal spatial coordinates.

[0006] The method of the present invention establishes a mapping relationship between geometric structure parameters and optical responses through a deep neural network. With the help of this neural network, the optimal structural parameters are generated according to the multiplexing phase requirements of the dual-function focusing meta-lens, and the design of polarization-multiplexed dual-channel focusing meta-lens in multiple near-infrared bands is completed. In addition, the method of the present invention innovatively uses a multi-wavelength Jones matrix to construct a structural database, so it can be easily migrated to the design of other wavelengths and polarization states. With the help of a deep neural network, the method of the present invention fully explores the potential of the structural parameter space and realizes independent focusing in any two polarization states. It can be widely used in the design of multifunctional photonic devices without the need for segmented, interleaved, or multi-layer design.

[0007] The technical solutions of the present invention are as follows:

[0008] A design method for a polarization multiplexing dual-channel meta-lens comprises the following steps:

[0009] 1) Randomly generate nanostructures and obtain their optical response data to construct an initial data set;

[0010] 2) Using the nanostructure parameters and their optical response data in the dataset to train a forward neural network, a forward prediction model from structural parameters to optical response was constructed;

[0011] 3) Using the trained forward neural network as a guide, train the reverse neural network to build a reverse generative model from optical response to structural parameters;

[0012] 4) Based on the design requirements of the dual-channel metalens, determine the operating wavelength, multiplexed polarization states, and focal space coordinates, and then obtain the phase profile required for metalens focusing;

[0013] 5) Based on the phase profile required for the metalens to focus, the inverse neural network recommends a nanostructure that meets the requirements to generate the metalens;

[0014] 6) Using a forward neural network to predict the optical response data of the meta-lens generated in step 5) to evaluate the device performance.

[0015] In step 1) above, the nanostructures in the initial dataset can be randomly generated by determining a parameterization scheme for the nanostructures based on the target optical properties of the dual-channel metalens. Alternatively, the nanostructures in the initial dataset can be generated based on a priori physical intuition and methods, or using a pre-optimization algorithm such as a genetic algorithm. The optical response data of the nanostructures can be obtained using numerical simulation software such as FDTD.

[0016] In the above step 2), the forward neural network training process is completed using the nanostructure parameters and their optical response data. The nanostructure and its optical response data are transmitted to the neural network, and the network node weights are adjusted using the gradient descent method so that the network output approaches the numerical simulation result of the input nanostructure.

[0017] In step 3), the use of a pre-trained forward neural network as a guide involves appending the pre-trained forward neural network to the reverse neural network during training to predict the optical response of the nanostructures recommended by the reverse neural network. During the reverse neural network training process, gradient descent is used to adjust the network node weights so that the output of the forward neural network approximates the input optical response data.

[0018] In step 4), the phases of the two multiplexed polarization channels can be calculated using the following formula based on the phase constructive condition of the generalized Huygens principle at the focus:

[0019]

[0020]

[0021] Where λ is the operating wavelength of the metalens, 1 and 2 denote the two multiplexed polarization channels. F1 (x1, y1, f1) is the focal coordinate of the first channel relative to the lens center; F2 (x2, y2, f2) is the focal coordinate of the second channel relative to the lens center.

[0022] In step 4), the modulation phase required for the dual channels is obtained based on the imaging requirements of the metalens. In step 5), this is used as the target optical response input into the inverse neural network. The inverse generative model trained in step 3) then recommends the required nanostructures. The entire metalens array can be composed of millions of unit structures, depending on the required size. Therefore, in this step, the powerful parallel computing capabilities of deep learning can be leveraged to sequentially obtain all target unit structures. Once all unit structures have been recommended, the entire metalens is complete.

[0023] In step 6), device performance evaluation using a forward neural network involves rapidly predicting the phase and amplitude responses based on structural parameters. The predicted phase can be compared with the target phase to verify the desired phase profile. The amplitude, on the other hand, can be used to assess device efficiency.

[0024] Furthermore, the data type in the initial data set described in step 1) should be tensor data to meet the training requirements of the neural network. The structural parameters can be parameterized as one-dimensional vectors, and the structural parameters can include shape parameters and optical parameters such as complex refractive index. To enhance the flexibility of the design, a broad spectrum Jones matrix can be stored during the construction of the initial data set. Then, when the design example is completed, spectral data can be extracted from the broad spectrum Jones matrix based on the operating wavelength and multiplexed polarization state, greatly reducing the construction time of the data set.

[0025] Furthermore, in step 2), during the training of the forward neural network, in order to avoid interference of phase periodicity on network training, the phase output of the network is set to the sine and cosine values of the phase. Since the mapping from structure to optical response is a single mapping, the forward prediction network can be trained directly. The number of data set samples and the network architecture will affect the learning effect of the neural network. The more samples there are, the higher the training accuracy will be, and the less likely it will be to have overfitting problems, but the more computing resources will be needed. According to the scale of the input data, it is necessary to adjust the learning algebra and learning rate of the neural network, and reasonably adopt dropout or regularization means to make it reach a balance between overfitting and underfitting, and the cross-validation method can be used to enhance the robustness of the neural network to the prediction of the new structure spectrum.

[0026] Furthermore, the phase profile described in step 4) is discretized. The position of the unit structure in the array is discrete, and its coordinates are substituted into formula (1) and formula (2) to obtain the phase profile. Considering that the nanostructure can interact with light at the subwavelength scale, and thus regulate the polarization state, amplitude phase and other properties of the light, the period of the unit structure should be at the subwavelength scale. The larger the size of the entire meta-lens and the larger the numerical aperture, the more practical it is. In order to avoid coupling between polarization states, the multiplexed polarization state selected in step 3) should be or close to an orthogonal polarization state, thereby ensuring that the phases of the two polarized lights can be independently regulated.

[0027] Furthermore, the role of the reverse generation network described in step 5) is to recommend structural parameters based on the target optical response. However, because there are multiple mappings from optical response to structural parameters, that is, there may be multiple different structures with the same or similar optical properties, it is very difficult to directly train the reverse generation network. Here, we use the forward prediction network as a guide to reduce the training difficulty of the reverse generation network. In principle, the input and output of the reverse generation network are opposite to those of the forward prediction network, so the two networks should adopt a relative and symmetrical structure. In the present invention, the reverse generation network is basically symmetrical with the forward prediction network, but because the reverse generation network is based on the dual-channel phase sine and cosine value recommendation structure, the output amplitude of the forward prediction network is only used for device evaluation, and the network loss function is set to the root mean square error of the four phase values.

[0028] The design method of the dual-channel meta-lens proposed in the present invention is the first method to design a polarization-multiplexed dual-channel meta-lens using a forward-backward neural network in combination with the wide-spectrum Jones matrix of the structure. The method of the present invention can start from the target phase requirements of the dual-channel meta-lens, and with the help of a reverse neural network, solve the required structural parameters to complete the device design. The focusing performance of the device can also be quickly evaluated through a forward neural network. The method of the present invention is flexible in design and can quickly complete the meta-lens design based on the required working wavelength, multiplexed polarization channels, and multi-focal space coordinates. The method of the present invention can be applied to the structural design of optical devices under multi-function or multi-constraint conditions, and has the advantages of high flexibility, strong robustness, wide applicability, and fast calculation speed. At a time when multi-function photonic device design paradigms such as segmented, interleaved, and multi-layer designs are commonly used, the design scheme proposed in the present invention will improve the working efficiency of the device and reduce noise crosstalk between multiple channels, and has a very broad market application prospect.

[0029] Compared with the prior art, the present invention has the following beneficial effects:

[0030] Compared with traditional design methods, such as parameter scanning and traditional optimization algorithms, the method of the present invention greatly reduces the consumption of computing resources and greatly reduces the difficulty of design. The parameter scanning method cannot recommend nanostructures outside the data set. Therefore, as the dimension of optical performance regulation increases, the nanostructures required in the data set increase exponentially, which is difficult to complete with the support of limited computing resources. Optimization methods such as genetic algorithms and particle swarm optimization algorithms have weak mobility and require a lot of time to optimize numerous nanostructures. They are not suitable for the design of non-periodic metasurfaces. Compared with traditional design methods, the design method of the present invention overcomes the above challenges and can efficiently design multifunctional metasurfaces with limited computing resources.

[0031] Compared with directly using structural parameters and spectral data to train deep neural networks, the present invention uses the wide-spectrum Jones matrix of the structure to construct the initial data set, which enhances the network's portability. Under given new working wavelengths and multiplexed polarization state conditions, the data set can be quickly extracted for network training, significantly reducing the computing resources required to construct the data set.

[0032] Compared to directly training the network using phase, this method uses the sine and cosine values of the phase as input and output, effectively avoiding the additional challenges caused by phase periodicity. Essentially, this is because there are some phases with different values but the same physical meaning, such as -π and π.

[0033] Compared to the segmented, interleaved, and multi-layered design paradigms of traditional multifunctional devices, this invention leverages deep neural networks to fully exploit the design potential of the structural parameter space, achieving dual-channel independent manipulation of the optical phase using the same set of metalens cells. While meeting the dual-channel focusing requirements, it significantly reduces noise crosstalk caused by spatial multiplexing using segmented, interleaved, and multi-layered structures, thereby improving the focusing efficiency of the metalens. This will provide new design ideas for integrated nanophotonics and complex multifunctional optical devices. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 Schematic diagram of the function of the dual-channel chiral focusing metalens designed in a specific embodiment of the present invention.

[0035] Figure 2 This is a design flow chart of a dual-channel chiral focusing metalens in a specific embodiment of the present invention.

[0036] Figure 3 Schematic diagram of focusing and light field distribution of four dual-channel chiral focusing metalenses at an operating wavelength of 1550nm in a specific embodiment of the present invention.

[0037] Figure 4 Figure 2 is a light field distribution diagram of a dual-channel metalens based on three other sets of orthogonal polarization states in a specific embodiment of the present invention (a), and a light field distribution diagram of a dual-channel chiral focusing metalens at operating wavelengths of 850 nm and 1024 nm (b).

[0038] Figure 5 The target phase profiles of 6 dual-channel chiral focusing metalenses designed in the specific embodiment of the present invention, as well as the predicted phase profiles and working efficiency diagrams of the metalenses obtained according to the designs. DETAILED DESCRIPTION

[0039] The present invention is further described below in detail through several design cases of dual-channel meta-lens with dual focal points in the near-infrared band in conjunction with the accompanying drawings, so that those skilled in the art can more clearly understand the present invention.

[0040] The functional schematic diagram of the designed dual-channel meta-lens is shown in the figure below. Figure 1 As shown, the two polarization components of the reflected light can be independently modulated and constructively focused at the desired position in space. In the present invention, any two orthogonal polarization states on the Poincare sphere can be used to realize the design of a polarization-multiplexed dual-channel metalens. Here, we use left-handed light (LCP, the north pole of the Poincare sphere) and right-handed light (RCP, the south pole of the Poincare sphere) as the dual-channel for multiplexing to demonstrate the design of a chiral focusing imaging metalens.

[0041] The working wavelength of the meta-lens is set at 1550nm, which can focus the left and right components of the reflected light on F L (x L ,y L ,f L ) and F R (x R ,y R ,f R ). Due to the interaction between the nanostructure and light, the phase of the reflected light will suddenly change relative to the incident light. Under the RCP light incident, the phase of the LCP reflected light suddenly changes to Similarly, under the incidence of LCP incident light, the phase of RCP reflected light suddenly changes to According to the generalized Huygens principle, combined with the working wavelength and the focal position, the phase value required to modulate the unit structure at the meta-lens (x, y) can be calculated from the above formulas (1) and (2). Traversing the spatial coordinates of the entire meta-lens unit structure, it can be calculated that and The phase profile that needs to be met.

[0042] In this case, the metalens' unit cell is a V-shaped gold nanostructure with a period of 400 nm. It consists of two 30 nm thick gold nanorods and can be parameterized by four structural parameters: (l1, l2, a, b), where l1 and l2 represent the lengths of the two gold nanorods, a represents the azimuth of the angle bisector between the two gold nanorods, and b represents the angle between the two gold nanorods. By adjusting these structural parameters, the polarization state, amplitude, and phase of light can be modulated.

[0043] The training dataset consists of 10,000 random nanostructures and their optical responses. The Jones matrix J(λ) of the target optical response can be obtained by finite element time-domain difference (FDTD) method (530 nm-1550 nm, step size = 1 nm).

[0044]

[0045] Where Rij is the complex amplitude of the i-polarization component under the j-polarization incident light. In a specific design example, the required light field data can be easily obtained by combining the Jones matrix with the polarization states of the incident and reflected light.

[0046]

[0047] represents the normalized Jones vector of the incident light polarization state, and represents the normalized Jones vector of the desired polarization state. Then for E out By taking the phase angle and amplitude, we can get the corresponding phase and amplitude values.

[0048] When training a neural network, the entire data set is split into 90% and 10% parts, respectively, as training samples and validation samples. The training samples are used to train the neural network, and the validation samples are used to verify the learning effect of the network. In this example, the forward prediction network input is a one-dimensional tensor (l1, l2, a, b) with a length of 4, and the output is the phase and amplitude data of left-handed and right-handed light. The forward prediction network can be trained by minimizing the root mean square error (MSE) between the optical response data predicted by the forward neural network and the optical response data in the dataset. The trained forward prediction network can predict the corresponding optical response based on the newly input geometric parameters.

[0049] Since there are different nanostructures in the dataset but with similar optical responses, it is a huge challenge to directly train the reverse generative network. Therefore, after the forward prediction network is trained, we use it as a guide to complete the training of the reverse generative network. The input of the reverse generative network is the target phase data. The output is the corresponding structural parameters (l1, l2, a, b). During the training process of the reverse generative network, the output structural parameters are input into the forward prediction network to obtain the predicted value of the optical property. Then, the difference between the target optical property and the predicted value of the forward prediction network is minimized to complete the training of the reverse generative network.

[0050] The design workflow of the chiral focusing imaging meta-lens is as follows: Figure 2As shown in Figure 2 , the forward and reverse networks are first trained using the required dataset. Then, based on the phase requirements for each coordinate point calculated using equations (1) and (2), the reverse generation network recommends the required nanostructure parameters. Due to the high computational efficiency of deep neural networks, a single nanostructure can be designed in under 1 microsecond. Finally, the forward prediction network can evaluate the performance of the generated structure to verify whether the realized metalens can achieve the intended function.

[0051] Based on the above workflow, at a working wavelength of 1550nm, if Figure 3 As shown in the figure, we designed four groups of chiral focusing meta-lenses according to four different focal positions, and their focal positions are a:F L (12,0,15)μm and F L (-12,0,30)μm for a); b:F L (12,0,20)μm and F R (-12,0,20)μm;c:F L (0,0,20)μm and F R (0,0,30)μmfor c); d:F L (0,0,20)μm and F R (0,0,20)μm. The scale bar in Figure d represents 4μm. Figure 3 The left side shows a schematic diagram of dual-channel light focusing, while the right side shows the light field distribution of the metalens in the xy and xz planes, as simulated using FDTD. The clear focal point demonstrates that the designed metalens can converge the reflected light from both channels to the pre-set focal point.

[0052] To further demonstrate the flexibility of the method of the present invention, we present a design demonstration of a dual-channel meta-lens based on other working wavelengths and other polarization states. Figure 4 As shown in a, we select three other orthogonal polarization states (A1 and B1, A2 and B2, A3 and B3) from the Poincare sphere, marked as state A and state B. Under the A polarization incident, the B polarization component of the reflected light is at the focus F B The reflected light converges at (12, 0, 30) μm. Under B polarization incidence, the A polarization component of the reflected light converges at another focus F. A (-12, 0, 15) μm. The light field distribution on the xy plane and xz plane was obtained through FDTD simulation, and the results were completely consistent with the design expectations. We further completed the design of chiral metalens with working wavelengths of 850nm and 1024nm, respectively. The focal coordinates are 850nm:F L (-12,-12,30)μm,F R(12,12,30)μm; 1024nm: F L (12,-12,30), F R (-12,12,30)μm. Figure 5 The forward prediction network is shown to Figure 3 mid-ad and Figure 4 The imaging performance evaluation results for the design case (b) include the target phase vs. achieved phase comparison, as well as the device's operating efficiency. All design cases demonstrate the expected dual-channel focusing efficiency. These design cases demonstrate the flexibility of our approach, enabling independent dual-channel phase modulation across a broad spectrum of stored wavelengths based on arbitrary orthogonal polarization states, thereby enabling the design of polarization-multiplexing metalenses.

[0053] The present invention combines bidirectional neural networks for the first time to design polarization-multiplexed dual-channel meta-lens. With the help of deep neural networks, the design potential of the structural parameter space is fully explored to realize the independent control of the phase of the polarization-multiplexed dual-channel. There is no need for segmented, staggered, or multi-layer design. The focusing imaging of the polarization-multiplexed dual-channel can be achieved using the same set of unit structures. With the rapid development of integrated nanophotonic devices today, the demand for multifunctional metasurface design is becoming more and more vigorous. The method of the present invention has extremely strong support and reference value for its future extensive development. The method of the present invention has the advantages of high degree of freedom, strong robustness, wide range of applicability, and fast calculation speed, and has important guiding significance for the design of complex multifunctional optical devices.

[0054] Finally, it should be noted that the purpose of disclosing the embodiments is to facilitate a further understanding of the present invention. Those skilled in the art should understand that various substitutions and modifications are possible without departing from the spirit and scope of the present invention and the appended claims. Therefore, the present invention should not be limited to the contents disclosed in the embodiments; the scope of protection claimed by the present invention shall be determined by the scope defined in the claims.

Claims

1. A design method for a polarization-multiplexed dual-channel metalens, wherein left-handed and right-handed light are multiplexed as dual channels for chiral focusing imaging. The unit structure of the metalens is a V-shaped nanostructure composed of two nanorods. The design method comprises the following steps: 1) Randomly generate nanostructures and obtain their optical response data to construct an initial data set. Specifically, the unit structure is parameterized into four structural parameters (l1, l2, a, b), where l1 and l2 represent the lengths of the two nanorods, a represents the azimuth of the angle bisector between the two nanorods, and b represents the angle between the two nanorods. By adjusting these structural parameters, the polarization state, amplitude, and phase of the light are modulated. First, the wide-spectrum Jones matrix J(λ) of the structure is obtained through time-domain finite element difference method: Where Rij is the complex amplitude of the i-polarization component under the j-polarization incident condition. The light field data is obtained by combining the Jones matrix with the polarization states of the incident and reflected light: in, represents the normalized Jones vector of the incident light polarization state, and represents the normalized Jones vector of the desired polarization state; for E out By taking the phase angle and amplitude, we can get the corresponding phase and amplitude values; 2) Using the nanostructure parameters and their optical response data in the dataset, a forward neural network is trained to construct a forward prediction model from structural parameters to optical response. When training the forward neural network, the input is a one-dimensional tensor (l1, l2, a, b) of length 4, and the output is the phase and amplitude data of left-handed and right-handed light: A L ,A R ; The forward neural network is trained by minimizing the root mean square error between the optical response data output by the forward neural network and the optical response data in the dataset; 3) Using the trained forward neural network as a guide, train the reverse neural network to build a reverse generation model from optical response to structural parameters; wherein the input of the reverse neural network is the target phase data The output is the corresponding structural parameters (l1, l2, a, b); during the training process of the reverse neural network, the output structural parameters are input into the forward neural network to obtain the predicted value of the optical response data, and then the difference between the target phase data and the predicted value of the forward neural network is minimized to complete the training of the reverse generation network; 4) Based on the design requirements of the dual-channel metalens, determine the operating wavelength, multiplexed polarization states, and focal space coordinates, and then obtain the phase profile required for metalens focusing; 5) Based on the phase profile required for the metalens to focus, the inverse neural network recommends a nanostructure that meets the requirements to generate the metalens; 6) Using a forward neural network to predict the optical response data of the meta-lens generated in step 5) to evaluate the device performance.

2. The design method according to claim 1, wherein: In step 1), a parameterization scheme for the nanostructure is determined based on the target optical properties of the dual-channel metalens, and the nanostructures in the initial data set are randomly generated. Alternatively, the nanostructures in the initial data set are generated based on a priori physical intuition and physical methods, or a pre-optimization algorithm. Then, the optical response data of the nanostructures are obtained with the help of numerical simulation software.

3. The design method according to claim 1, wherein: Step 2) The training process of the forward neural network is to pass the nanostructure and its optical response data to the neural network, and use the gradient descent method to adjust the network node weights so that the network output is close to the numerical simulation result of the input nanostructure.

4. The design method according to claim 1, wherein: Step 3) The trained forward neural network is suffixed to the reverse neural network to predict the optical response of the nanostructure recommended by the reverse neural network; during the training process of the reverse neural network, the network node weights are adjusted using the gradient descent method so that the output of the forward neural network approaches the input optical response data.

5. The design method according to claim 1, wherein: Step 4) Based on the constructive phase condition of the generalized Huygens principle at the focus, the phases of the two multiplexed polarization channels are calculated using the following formula: Where λ is the operating wavelength of the metalens, 1 and 2 are marked as two multiplexed polarization channels; F1 (x1, y1, f1) is the focal coordinate of the first channel relative to the center of the lens; F2 (x2, y2, f2) is the focal coordinate of the second channel relative to the center of the lens.

6. The design method according to claim 1, wherein: Step 6) The forward neural network predicts the phase and amplitude responses, and the predicted phase is compared with the target phase to verify the required phase profile; the amplitude is used to evaluate the operating efficiency of the device.

7. The design method according to claim 1, wherein: The unit structure of the meta-lens is a V-shaped gold nanostructure composed of two gold nanorods.

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